19 63ApJS. . . .8. .17 7P larger flares.Ifoneadoptsthispointofview,then thequestionofenergysupplyfor house ofthermalenergyinthesolarinterior. The latterappearsdubiousbecauseof liberates theenormousquantitiesofenergyconsumedintotalflare,orwhetheritis processes occurringinthesolaratmosphere.Attimeofaflare,thereisvisible be insitusomelatentformorsuppliedby aviolenteruptionfromthevaststore- The viewisbased,quitereasonably,ontherather explosivepropertiesofmanythe some uniquedynamicalprocesswhichsuddenly makes availablehithertolatentenergies. one proceedtolookformechanismsexplain thedetailedoperationofflare. degree allthetime.Onlyafteraprovisionalanswer hasbeengiventothisquestioncan activity, accelerationofelectronsandionstosubrelativisticrelativisticenergies,etc. X-ray emission,enhancedcoronalheating,explosiveoutburstsofmatter,prominence constitutes thevisibleflare.Therearealsoenhancedradio-noiseemission, brightening inlineemission,seenbothagainstthediskandprofileatlimb,which merely anintensificationofsomethinglikecoronalheatingwhichisgoingoninsome further, theintensityofindividualflaresformsacontinuousspectrumextendingall occur inwidelyvaryingproportionsfromoneflaretothenext.Tocomplicatematter the flareseemstotakeondefiniteshape,viz., the energyforexplosionmusteither way downtowhatareonlybrightplages.Thusthetheoreticalproblemofunderstanding under grantNASA-NSG-96-60. the flareisinfactoccurrenceofsomeuniquedynamicalprocesswhichsuddenly the solar-flarephenomenonpresentsmanyfacets.Oneofbasicquestionsiswhether Observation doesnotyetmakecleartheinterrelationofthesevariousprocesses.They earlier discussionsoftheproblemarecited.Sincenopossibleenergysourceotherthanmagneticfields if themergingmagneticfieldsareexactlyantiparallel.Noneofknownmechanismssufficiently theoretical mechanismsforthediffusion,reconnection,andannihilationofmagneticfieldsispresented. behef thatthesolar-flarephenomenonisadirectconsequenceofannihilationmagneticfieldson gest thatotheralternativesfortheflaremustbeexplored. field annihilation,areconsidered.Itisshownthattherenoreasontoexpectrunawayelectronsand has yetbeendeveloped,thequestionoffieldannihilationremainsbothopenandpressing. rapid toaccountforthesolarflarefromannihilationofmagneticfields.Errorsandomissionsin mechanism. ItisshownthatSweet’smechanismmuchmoreeffectiveinahighlycompressiblemedium The mechanismsdiscussedareJouledissipation,ambipolardiffusion,andvariousformsofSweet’s the sun.Thereisverylittleinobservationstosupportsuchviews.Asystematicstudyofknown effective instabilityunlessthefieldsareexactlyantiparallel. At thepresenttimepopularviewseemsto be thataflareoccursastheresultof The solar-flarephenomenonismadeupofalooseassociationdiversedynamical The paperpresentsastudyoftheobservationsandtheorywhicharerelevanttopresentlypopular The observationalandtheoreticaldifficultieswiththehypothesisofmagnetic-fieldannihilationsug- The possibilitiesofrunawayelectronsandhydrodynamicinstability,asmeansforhasteningmagnetic- * ThisportionoftheworkwassupportedbyNational AeronauticsandSpaceAdministration National CenterforAtmosphericResearch,Boulder,Colorado,andEnricoFermiInstitute © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Nuclear StudiesandDepartmentofPhysics,UniversityChicago,*Chicago,Illinois THE SOLAR-FLAREPHENOMENONANDTHEORYOF RECONNECTION ANDANNIHILATIONOF MAGNETIC FIELDS Received NovemberP,1962 I. INTRODUCTION E. N.Parker ABSTRACT 177 19 63ApJS. . . .8. .17 7P 1 9 202 172 32 301 problem inthepastdecade,andmanyinterestingideashavebeenturnedup(seediscus- popular beliefthatthenecessaryannihilationofmagneticfieldshasbeenaccountedfor sion inCowling1953ofsometheearlyideas).Indeed,thereappearstobe is tounderstandthemechanismbywhichmagneticenergy,containedpresumablyin violent disturbanceinthephotospherebeneathvisibleflare.Theassumptionthat rises toamaximumusuallywithin1-15minutes,thereafterdeclining,givetotallife inadequate byseveralpowersof10tosupplytherapidenergyconsumptionflare The theoreticalobjectionsarebasedonthefactthatwhenknownmechanismsfor by quantitativetheory. reason thatthermalenergiesformtheonlyapparentalternativeandarecompletelyin- much moredifficulttoobserve, anditcannotbestatedatthepresent time whatisthe fainter portionsoftheflare(seediscussionandphotographsinKiepenheuer1953 presented initalics. idea thattheenergyforflarecomesfromannihilationofmagneticfieldswillbe of thepresentlyknownmechanismsforannihilationmagneticfields.Numericalex- the conversionofmagneticenergyareworkedoutquantitatively,theyfoundtobe both theoreticalandobservational,withtheideathatsolarflareissimplyaconse- quickly intothermalenergyoritsequivalent.Agreatdealofthoughthasgonethis adequate. Onthebasisoftheseideas,centralproblemintheorysolarflare sign ormagnitudeofits contribution.Theextraemissioninthelinesindicates aradia- enhanced, sothattheystandoutclearlyagainst thephotosphere,butcontinuumis extremely faintcomparedwiththesolardisk. Many oftheemissionlinesarestrongly magnetic spectrum,butinpracticethisisvery difficultbecausetheflareisusually radiative outputcanbeestimatedinprinciple byintegratingovertheentireelectro- sudden brighteningofactiveloopprominences over theassociatedsunspotgroup. a luminouscloudashighitisbroad,withcharacteristic verticalscaleof2X10cm something oftheorder0.5X10cmfor largest.Theemissionregionisevidently brightening ofplagesatsomedistancefromtheflare.Theemissionvisibleflare amples aregiveninthelastsectiontoillustrateinadequacyofmechanisms. observational objectionsareratherstraightforwardandwellknowntomanyobservers. quence ofthesuddenannihilationmagneticfieldsinanactivesunspotregion.The the verystrongfieldsassociatedwithsunspotsnearflare,canbeconverted the energyisinitiallyinsituleadstoconclusionthatitmagneticenergy,for the failureofmostflarestobevisibleinwhitelightandbecauseobserve order of100-400km/sec.Thevisibleareas flares rangefromaslittle10cmto of theorderhalfanhour.Theratesextension ofbrighteningarecommonlythe Athay andMoreton1961).Thereisalsotheinterestingphenomenonofsympathetic and, infact,itisnoteasytodefinethedifferencebetweenabrightplageandsomeof of oppositepolarityinanactivegroup.Thebrighteningalwaysoccursaplageregion, spheric lineemission,showingusuallyacontortedregioninamongtheindividualspots occurring atthetimeofvisibleflare.Theobservationswhichseemtocontradict tive outputoftheorder of 10ergsduringthelifeaverylargeflare(Parker 1957¿;)and total energyexpenditure,(ii)themagneticenvironment,and(iii)changes We payparticularattentiontothoseobservationswhichgiveanindicationof(i)the Some alternativepossibilitiesaresuggestedanddiscussedverybriefly. (Parker 1957í;).Thebulkofthepaperisdevotedtoanextendedquantitativeexposition (Warwick 1955).Whenseeninprofileonthesolar limb,theflareoftenappearsas 178 E.N.PARKER 10-10 ergsduringthe morecommonclass2flare(BillingsandRoberts 1953). 1 It isnoteasytoestimatethetotalradiative output fromasolarflare.Thetotal It isthepurposeofpresentpapertoshowthat,infact,thereareseveraldifficulties, Against thediskofsunvisibleflareappearsasabrighteninginchromo- Let usreviewsomeofthegrossobservationalfeaturessolar-flarephenomenon. TheauthorisindebtedtoProfessor R.G.Athayforthisimportantpoint. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 19 63ApJS. . . .8. .17 7P 113 4 4 10 42 5 30 2 43 3-10 6 3 3 3 3 -63 32 3 15 irregular gasmotions. istics, suchasverybroadwings.Thewingshaveledsomeinvestigators(see,for gives risetothetypeIVandVradioburstsobservedinassociationwithvisibleflare. site ofthevisibleflarewithvelocitiesorder1000-2000km/secacrossdisk broad wings,iftheyrepresentDopplerwidth,aremoreprobablytheresultofhigh-speed instance, Tandberg-HanssenandZirin1959)tosuggestgastemperaturesmuchhigher a fewtimes10electrons/cm,withtemperaturesomewherebetweenoneandtwo atoms present.Theemissionlinesfromthevisibleflareshowmanypeculiarcharacter- active regioncopiousquantitiesofrelativisticelectrons,whosesynchrotronradiation of thesun(AthayandMoreton1961)duringexplosiveonsetflare.Thedis- times 10°K.Itfollowsthatthegasishighlyionized,sothereareveryfewneutral into interplanetaryspace,wheretheyareobservedattheorbitofearth.Thepeakflux than the1-2X10°K.ItispointedbyJeffriesandOrrall(1961a,6),however,that The energyspectrumoftheprotonsissufficientlysteepthatmostparticle There areacceleratedalsolargequantitiesofpositiveions,someportionwhichescape is nearthelowestobservedenergy.Aprotonof30Mevhasavelocityabout0.7X10 of energeticprotonsaboveabout30Mevmaybe10protons/cmsec(see,forinstance, tances upto4X10kmfromtheflare. turbances arepresumablyresponsibleforthetemporaryfadingofprominencesatdis- 1959; JeffriesandOrrall1961a,b)thatthemeandensityinvisibleflareisperhaps is oftheorder10ergs. in interplanetaryspace.Assumingthattheparticlesattimeofpeakintensity which ismorethan10timesgreaterthenormalgalacticcosmic-rayenergydensity cm/sec, sothataparticlefluxof10protons/cmimpliesdensitytheorder Meyer etal.1956,andthesummaryofprotoneventsinMahtsonWebber1962). visible hemisphereofthesun.Theinferenceisthatblastwaveoriginatedatsun earth occupied1cubica.u.,itfollowsthattheenergyofsolarprotonsabove30Mev of 3XlO^/cmandatotalenergydensitytheorder1.6lOergs/cm, mosphere toseveraltimes10°K.Thevelocityoftheblastwaveininterplanetaryspace at thetimeofflare,presumablyfromexplosiveheatinglocalsolarat- for instance,Parker1962),usuallylastsseveral hours,suggestingthattheblast-wave after theflare.Theblastwaveisresponsibleforgeomagneticstormand is inferredtobe1or2times10km/sec,basedonthearrivaltimeatearthdays blast wavessuggest,too,thatthethicknessisprobably notlessthan0.1a.u.Altogether, magnetic storm,duringwhichtimetheblastispressing inonthegeomagneticfield(see, number oflargeflaresonthevisiblehemisphere of thesun,blastwavemustberather with whichthegeomagneticfieldisbuffetedby suchablastwave,comparedwiththe broad, occupyingatleast1steradianasseenfrom thesun.Theinitialphaseofgeo- reasons. Using30protons/cm , whichisatbestonlyanorder-of-magnitude estimate, 30 atoms/cm.BlackwellandIngham(1961) suggest 300atoms/cmonthebasisof an assumedvelocityof1500km/sec,thatthe densityofthewaveisorder earth. Theobservedcompressionofthegeomagnetic fieldsuggests,inassociationwith Forbush decreaseinthegalacticcosmic-rayintensity.Judgingfromfrequencywith yields akineticenergy density of0.6X10ergs/cm,atotalenergy of 2X10ergs, then, theblastwaveoccupiesavolumenotless than0.1a.u.asitreachestheorbitof thickness isatleast0.1a.u.Theoreticalconsiderations (Parker1961)ofinterplanetary and atotalmassof2X 10 gm.Notethatthetotalenergyisatleastas largeasanyof their zodiacallightobservations, buttheobservationseemsalittledubious forseveral the estimatesofenergy intheotherfeaturesofflare,sothatwe mayconjecture Analysis oftheemissionlinesandcontinuumsuggests(Jeffries1957;Jeffriesetal. It hasbeenobservedthathydrodynamicdisturbancessometimesemanatefromthe At thetimeofvisibleflarethereareacceleratedsomewhereinvicinity It isobservedthatablastwaveoftenarrivesatearth1or2daysafterflareonthe © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem SOLAR-FLARE PHENOMENON179 180 K N. PARKER that one of the principal manifestations of a large solar flare is an interplanetary blast wave. It is not clear whether the interplanetary blast wave has any connection with the sudden expulsion or surge of gas from the flare during the explosive phase (Athay and Moreton 1961) or whether it arises solely from the expansion over a larger period of time of the enhanced corona associated with the active region and the flare. We are inclined to the view that, whether there is any connection with the surge or not, a major portion of the energy and momentum of the interplanetary blast wave is imparted by expansion of the enhanced corona. This completes the summary of the observed and inferred properties of the solar flare. We take 1032 ergs as a very rough order-of-magnitude estimate of the energy expenditure in a large (class 3) flare event. This amount of energy corresponds to a mean flux 2 X 109 ergs/cm2 sec through a typical large visible flare area (if, in fact, the visible flare area has any relevance at all) of 5 X 1019 cm2 for a typical characteristic flare life of 103 sec. This energy flux may be compared with the flux of radiant energy 6 X 1010 ergs/cm2 sec from the photosphere and with the estimated chromospheric and coronal heating requirement of 108 ergs/cm2 sec. In terms of magnetic energy, 1032 ergs is equivalent to the complete annihilation of a 500-gauss field occupying a cube 2 X 104 km on a side, or 100 gauss over a cube 6 X 104 km on a side, or the reduction of a 500-gauss field to 400 gauss over a cube 3 X 104 km on a side, etc. These numbers serve to illustrate the magnitude of the magnetic changes that might be expected in a flare sight if the flare energy is magnetic in origin. Magnetic observations of active regions have been carried on for some time (Hale el al., 1919; Babcock and Babcock 1955; Babcock 1959), but only recently have the sensitivity and resolution been sufficient to see the variations in field across the site of a flare. And, of course, there is need for considerable further improvement before some of the existing questions can be resolved. Briefly, Severny (1958) reports that flares seem to occur near regions where the longitudinal component of the magnetic field shows a reversal in sign and that the magnetic field is significantly changed during the course of the flare. Evans (1959) finds much the same thing except that in his observations the field returned quickly to its initial value during the declining phase of the flare. Evans esti- mated the magnetic change to be of the order of 4 X 1031 ergs during a class 1+ flare, before the sudden return to the initial value. Howard and Babcock (1960) also find no net change in the magnetic field over the course of the flare. Hanson and Gordon (1960) have shown that succeeding flares in an active region may occur with identical visible profiles and shapes, suggesting that if the flare shape is determined by the local magnetic-field con- figuration, then the field is not changed much from one flare to the next. Then there is the remarkable observation that the time dependence and magnitude of the X-ray emission (Fortini 1963) and of the radio emission (de Feiter and Fokker 1961) are the same for a sequence of flares in the same site, whereas they are strikingly different be- tween flares in different sites. The observations all suggest that in some way succeeding flares follow some blueprint that is characteristic of the site in which they occur. The blueprint does not seem to be destroyed by the individual flares. Altogether, then, it would seem that there is very little in the direct observations of solar magnetic fields to support the notion that the flare is generated by the catastrophic annihilation of magnetic fields. We turn now to the question of whether there is any known theoretical mechanism that might permit the annihilation of magnetic fields on the scale observed on the sun to produce 1032 ergs in the short period of lOMO3 sec seem- ingly required by the visible flare. Since the problem of the annihilation and reconnec- tion of magnetic lines of force is a subject of some interest in itself and has been con- spicuously neglected in spite of its importance to a number of natural phenomena, it will be developed at some length in the sections which follow. A brief listing of the known processes for the diffusion, reconnection, and annihilation of magnetic lines of force will serve as a guide through the theoretical sections that fol- low. Application of the theory to specific phenomena, such as the solar flare, is given in Section IV.
© American Astronomical Society • Provided by the NASA Astrophysics Data System 19 63ApJS. . . .8. .17 7P 3 2 3 2 ion collisionfrequencies with theneutralatomsbyvandVi,respectively. Thenthefric- of collisionstheionizedcomponentwith neutral atoms.Denotetheelectronand ionization, A,sothattheionandelectrondensitiesareN{=NANparticlesper increase thediffusionratebymanyfactorsof10inatenuous,partiallyionizedgas large undermostastrophysicalcircumstances. usual statementthatthemagneticReynoldsnumber,Lvc/â(Elsässer1954),isvery interest inmostsolarandastrophysicalphenomena;thisremarkisequivalenttothe out thatthereconnectionoflinesbyresistivediffusionismuchtooslowtobegreat resistivity ofthegasinwhichfieldisimbedded.Ifwritten1/ít(esu), velocity v.Thephysicalessenceofambipolardiffusionissimplythatthemagneticfield conductivity residesintheionizedcomponent,ofcourse,soregardcompo- discussion. ConsideragasofNneutralatoms/cmwithrelativelyslightdegree used insomeofitsapplications,sowefeelthatanelementarypresentationfroma greatly increasetheeffectiveresistivity. There isthepossibilityofrunawayelectrons,leadingtoplasmainstabilitiesthatmay closely, decreasingthescaleZ,andincreasingdiffusionrate(Sweet1958a,b).Thereis is squeezedoutfrombetweentwoantiparallelfields,allowingthemtoapproachmore given above.Forinstance,thereisthephenomenonofambipolardiffusion,whichmay sistive reconnectionoflinesforcemaybefoundinParkerandKrook(1956).Itturns Dcf/c andcharacteristicvelocityg/
db (25) 1 — ub
« dÔ e(Ô)
1 2 > (7+1) / (1 - J)(!-k)/2 (26) 2(y-i)nci -y)S where £1 is the position at which b becomes equal to 1.0. It is obvious that the distance £1 — £ beyond £ at which b reaches 1.0 is finite for all 0 < 7 < 1. Hence for 0 < 7 < 1 the magnetic field B and the velocity v reach Bq and z;o at some finite distance from the center of the transition. Beyond £1 the solution is just the uniform drift v = vq, B = Bq all the way to the outer boundary of the region of field. Note that, for 7 = 0, £1 has the value 1.7; for 7 = 0.5, £1 is something of the order of 3. For 7 = 1, £1 is infinite, but the value of db/d% at £ = 0 is 1.0. This fixes the scale l of the transition region as O^/zio) for all 7 between 0 and 1.0, as assumed in the earlier order-of-magnitude treatment. It is possible to use equation (24) in combination with equation (23) to obtain a better approximation for S than that given by equation (23) alone. Requiring that equations (23) and (24) join at, say, £ = 0.9 leads to S = 0.87. The value 0.93 was obtained from equation (23) alone, indicating only a 7 per cent correction. It is important to note, for the approximate solutions that follow in the next section, that the approximation repre- sented by equation (22) gives a fairly good approximation for S for all values of 7 from 0 to 1.0. For 7 = 0, equation (22) gives Sb = tanh (u/S), so that 5 = 0.833. This is to be compared with the exact value S = 0.76. For 7=1, equation (22) is exact, giving u = b and S = 1.0. Altogether, then, we have the results S = 0.76, S = 0.87, and S = 1.0 for 7 = 0, 0.5, and 1.0, respectively. The merging velocity v0 is computed from the definition of S as a / CoA1/2 Vo= ~s\ir) •
This expression differs from the order-of-magnitude value (10) by a factor of the order of only 2 or 3. Note that S varies only about 30 per cent between 7 = 0 and 7=1. It follows that vo varies only by about 30 per cent and is relatively insensitive to 7. The physical reason for the insensitivity is that most of the fluid squeezes out from between the fields near x = 0, where b2 is rather less than 1. The factor (1 — b2)7 is then approxi- mately 1.0 regardless of the value of 7. The function u(b) is plotted in Figure 2 for 7 = 0, 0.5, and 1.0. The curve labeled 7 = 0.5 is computed from equation (23). The unlabeled curve is the composite of equations (23) and (24) for 7 = 0.5 joined at £ = 0.9. The functions u(£) and 6(£) are given in Figure 3. As we have already noted, the present calculations are approximate because they are based in part on equation (20). We have shown that there is no critical dependence of the merging velocity ^0 on 7. Nonetheless, it would be instructive if the exact stationary equations could be integrated on a machine. Not only would such a computation check the detailed accuracy of the values of ^0 obtained in the present discussion, but presum- ably they would show quantitatively the flow pattern of the fluid squeezing out from between the fields, which the present formulation is forced to avoid. Because of the interest in the exact problem, the dynamical equations are noted in Appendix II.
© American Astronomical Society • Provided by the NASA Astrophysics Data System SOLAR-FLARE PHENOMENON 191
c) Incompressible Flow, Ambipolar Diffusion When ambipolar diffusion is present, we must add to equation (15) the second term on the right-hand side of equation (7), so that the equation equivalent to (19) becomes db _ l — ub (28) Jl~ l + g2ô2’ where q2 = Bq2/{^ttkv), representing the ratio of ambipolar diffusion to Joule dissipa- tion. Assume q to be constant, then in place of equation (21) we have
2 2 du= (l-62Ml + g ¿ ) db 1 — ub
Fig. 2.—Plot of u(b) in incompressible flow with Joule dissipation for 7 = 0, 0.5, and 1.0 in eq. (20). The unlabeled curve, in two pieces, is the approximate form obtained by joining eqs. (23) and (25) at £ = 0.9.
Fig. 3.—Plot of «(£) and b{£) in incompressible flow with Joule dissipation for 7 = 0, 0.5, and 1.0 in eq. (20).
© American Astronomical Society • Provided by the NASA Astrophysics Data System 19 63ApJS. . . .8. .17 7P 2 2 21/ 2 2 If ambipolardiffusionisimportant,then#)>>1,and1maybeneglectedcomparedwith qb exceptfor6<1/#.Inthisregion,Z>1/^,wehave The firsttermintheparenthesesrepresentsnarrowlinearportionofcurve the vicinityoforigin.ItwasshowninSectionIIthatwecanignoreit,limit 192 E.N.PARKER panding u(b)as fields elsewheremby>l/q.Thusweconfineourattentiontosolutionof The resultingfunctionsu(b)areplottedinFigure 4.Analternativecomputation,ex- where K=qS. of largeq,withoutsignificantlyaffectingthecomputationmergingvelocityor The correspondingvaluesofKareindicated. [(1 +8K)—1]8.Joiningthesolutionsfor b (38) no+l-l?2 where ds(l - s2) s2 I(b,ß)= i" (39) J 2 o (n0+l-s )ß' The integral / (b, ß) is easily evaluated for integral values of ß, /(¿,0) = P3-LÔ5, 3 1 2 I(b, l)=Woô + P -|Wo(l+«o) / ln||±^^|, l T(h ^ _2b*-b(2 + 3n0) . 2 + 3»o , (l+«o) ^+0 M J 2 1 1 2 1 2 2(w0 +1 — ö ) ‘ "4(l+«0) / (l+wo) / -^’ T(h nob ^ (4 + 5wp) b M ; 4 ( Mo + 1 — i»2 )2 8 ( 1+ »o) ( 1 + «o — Ô2 ) 1 2 4 + 3m0 , (1+mo) / +0 3 2 In 1 2 16( 1+ m0) / (l+wo) / - 6' It then follows that /(1,0)=Ä, /(l, 1) =¿-AMoln- + 0(Mo) xo Mo 7(1, 2) = 5 In | + O(M0ln m0), Mo 7(1, 3) =~r i In —+ 0(MolnMo). 4^o n0 To determine R, put u = b = 1 in. equation (38), obtaining no R2 = (40) %+Q2m,ß)' In the absence of ambipolar diffusion (Q — 0) this reduces to R2 = 3no/2. In the pres- ence of strong ambipolar diffusion (Q 1) the result is R2Q2 = wo//(l, ß), and for ß = 2 2 2 2 0, 1, 2 the result is R = 15no/2Q , 3no/Q , 2no/Q In 4/w0, respectively. Since the merg- ing velocity vo is proportional to l/i£, it follows that, with or without ambipolar diffusion, the merging velocity is enhanced by a factor l/^o1/2 in the presence of high compressibil- ity {no <$C 1). As noted previously, the physical basis for the enhanced merging velocity is the high rate at which matter in compressed form is squeezed out from between the two fields. The density Nm, where the fluid is squeezing out, is so large compared with the density No being carried in by v{x) that only a very thin (scale l) transition region is required in which to squeeze out the material. A thin transition region leads to more rapid diffusion. © American Astronomical Society • Provided by the NASA Astrophysics Data System 19 63ApJS. . . .8. .17 7P 2 2 2 2 2 2 from equation(36).For1—ôrathergreaterthanwo,(36)reducesto from equation(36),providedonlythat1—¿>>n^. becomes justifies thefirstpartofapproximation,inwhichfactor1—ubwasomitted in thelimitofsmallIntegratingthisequationleadstoub<0(wo6),demonstrating note byisinfactsmall,aswehavesupposed.Then,neglecting3Î,obtaine= u =1—eand<5againexpandaboutthepointb1.Equation(36) side ofthedifferentialequationisnegligiblewhen1—Z> (£)=1leadsto£^Q,whichwetakerepresentthethick- for ß=2.Theserelationsareapproximatelyvalidonlyin0<1—wo,becauseof for ß=1;and for jS=0; the neglectof1—ub.InregionKno 2. Hydrodynamic instability.—Now consider the possibility of hydrodynamic in- stability in the thin sheet of material squeezing out from between the two merging fields. Keeping with the notation used so far, the fluid is flowing in the y-direction in a thin sheet of thickness 21 centered about æ = 0. The magnetic field on each side of the fluid sheet is also in the y-direction. One may imagine two distinct unstable transverse wave motions that could arise, one with its wave vector in the y-direction and the other with its wave vector in the z-direction. The wave with its vector in the y-direction leads to waves in the fluid sheet and in the lines of force. The perturbations are essentially Alfvén waves propagating along the fluid sheet and the neighboring field. We have been unable to demonstrate, on the basis of simple models, how such waves will significantly enhance Fig. 6.—Schematic representation of the section y = 0 through the merging antiparallel regions of field. The magnetic lines of force are perpendicular to the plane of the page and in {a) have one sign above the z-axis and the opposite sign below, as indicated by the two different crosshatchings. The first diagram {a) represents the unperturbed situation, with the heavy line along the axis indicating the transition region between the two fields. The second diagram (6) represents the exchange perturbation of wave- length X and amplitude s, carrying fines of force deep into regions of opposite sign. the dissipation. Their only obvious effect is to consume energy that might otherwise have gone into the flow of fluid out of the transition region, thereby inhibiting Sweet’s mechanism. The wave with its vector in the z-direction, on the other hand, exchanges magnetic flux between opposite sides of the transition while doing little or no work on the field. The situation is shown in simplified form in Figure 6. The heavy line across the middle of Figure 6, a, represents an end view, looking in the y-direction, of the unper- turbed transition region. The two crosshatchings represent magnetic fields of opposite sign, the field being perpendicular to the plane of the page. The perturbed field is illus- trated in Figure 6, b, where the transition region is carried into a sinusoidal wave of large amplitudes. If the field is assumed to be of great length in the y-direction (perpendicular to the page), then negligible work need be done on the field. If the wave length X of the perturbation is large compared with the thickness l of the transition layer, as illustrated in Figure 6, then the diffusion is enhanced because the transition layer is stretched to greater length, by the factor (1 + s2A2)1/2> assuming that l is relatively unaffected. If © American Astronomical Society • Provided by the NASA Astrophysics Data System 19 63ApJS. . . .8. .17 7P 162 2 2 2 low impedance,external electromotiveforceacrosstheplasma.Itisnot obviousthatthe vicinity ofthecurrent.Pinchesareproducedin laboratoryplasmaswithahighvoltage, for ionizedhydrogen.Forambipolardiffusion,useequations(48)and(49),puttingWi= plicable, andthequestion issimplywhetheranyviolentmagneticinstabilities arelikely. In theabsenceofanexternal electromotiveforce,thehydromagneticequations areap- astrophysical situationis atallanalogous,becausethereisgenerallyno externalelectro- This questionhasbeen discussed, thoughperhapsinadequately,inthe foregoingpara- motive force.Thereare onlyinducedelectromotiveforcesavailableto drivecurrents. power everythingelseandcauseaviolentcontraction ofthefieldsandplasmain and equation(49)forß=2gives a =SkT/M.Then,withAi10~cm,equation(48)forß1gives polar diffusion.ForJouledissipationitfollowsthat respectively. ItisobviousthatifLandNoaresufficientlysmall,thetransientdissipa- ratio isoftheorderunity,effectwouldbelarge.Thel/Lgivenbyequa- estimated inequation(32),andthedissipationwouldproceedcorrespondinglyfaster. gas wouldcompresstothedensityN,formingatransitionlayermuchthinnerthanl amplitude (s>X),theshortestscaleisX,andfieldswilldissipatetoadistances the wavelengthshouldprovetobesmallcomparedwith/,thennotethat,forlarge directed fieldtosuchanintensitythatthestresses oftheself-fieldcurrentover- characterized by(L/vo)(l/Lno)=l/mvo. appears onlyinthelogarithmandhasverylittle effectwhenno<£l. tion beforeasteadystateisreachedmaybeimportant. WithJouledissipation,small tions (11)and(44)forJouledissipationbyequations(12),(48),(49)ambi- The importanceofthisinitialtransientdissipationdependsontheratiol/Ln^.If small portionofthefieldwouldbeannihilatedbeforenecessaryaccumulationgas The totalamountofmaterialinthefieldinitiallyisLNq.IflN< 2 <2 Bo2+B^ N(x)N kTL'T -i¡ B (x) +Br Z (x) = NokT'L'T' -\« (54) 0 0 Stt At the center of the transition region, the field in the y-direction, which has been denoted 2 by F>(#), vanishes. Putting Bz(x) ^ Bi[N(x)/Ni] and neglecting NokT and Bi /8ir com- pared with Bq2/8tt, the relation can be solved for N(0) to give N(0) _ n 2 0 (54a) 2 Nm 2s where N(Ú) is the gas density at # = 0, Nm = B^I8tt1zT is the gas density at x = 0 if there were no field in the 2-direction, and s is the ratio B\IB§{<£X). The merging velocity given by equation (32) is reduced by the square root of this ratio iV(0)/iVm, plotted in Figure 7 as a function of Roughly speaking, A^O) is significantly less than A"™, and the merging velocity is significantly reduced by Bi, if s > no. For s ^>> ^o, we have 1/2 N(Q)/Nm~ uq/s, so that is reduced from equation (11) by (i?o/£i) . Since wo = Nv/Nm may be as small as 10-5 in such places as the solar atmosphere, it is evident that even very small deviations of the two merging fields from antiparallelism may seriously impede their annihilation. IV. APPLICATIONS a) Annihilation of Solar Fields Consider the rate at which magnetic fields may be annihilated in the solar atmosphere by ambipolar diffusion and by Sweet’s mechanism. 1. Photosphere.—In the solar photosphere, where T ~ 6000° K and one atom in 103 or 104 may be ionized, the electrical conductivity is of the order of 1012 esu. The diffusiv- ity v = £2/47r<7 is, accordingly, of the order of 108 cm2/sec. The ambipolar diffusion co- efficient B2/^ttk = B2/4cTrNiNaMiA¿Wi may be estimated in specific cases. The picture is complicated by the presence of both positive and negative ions, the positive ions being largely metallic in the cooler layers; but this need not concern us in making the present rough estimates. To obtain an order-of-magnitude estimate of the ambipolar diffusivity, put Wi = {8kT/M)l!2. Then remember that the effective value of B2/8tt available for driving the ions through the neutral gas cannot exceed the strength of the neutral gas to 2 resist, i.e., B /8t < NakT. It follows that the ambipolar diffusion coefficient is bounded by B2 < 2wi (55) Ltt/c ~ 2>NiA i' The temperature must be below 104 ° K if the medium is to be largely un-ionized, so that, for hydrogen ions, Wi does not exceed about 106 cm/sec and, for metallic ions, 2 X 105 cm/sec. Put Ai = 10~16 cm2. Then, for metallic ions, the ambipolar diffusion coefficient is not more than 1.3 X 1021/A'¿ (cm2/sec). A typical value for A7"» in the visible photosphere is 1013/cm3, with Ni generally decreasing upward throughout the entire region (see, for instance, Münch 1953). The result is 1.3 X 109 cm2/sec as an upper limit © American Astronomical Society • Provided by the NASA Astrophysics Data System 204 E. N. PARKER on ambipolar diffusion in the photosphere. Comparing this with the 108 cm2/sec esti- mated for the diffusion due to ohmic resistance, it follows that ambipolar diffusion is evidently no more important in the photosphere than Joule dissipation. Elsewhere in the sun we would expect ambipolar diffusion to be even less important because of the higher degree of ionization. To obtain a rough upper limit for the rate of Sweet’s mechanism in the photosphere, put B = 103 gauss in a typical density of 1017 atoms/cm3. For such values the gas pres- sure is somewhat larger than the magnetic pressure, so that, to a first approximation, the 5 expression (26) may be employed with S = 0.87. With C0 = 7 X 10 cm/sec and v ^ 108 cm2/sec, it follows that |^o| = 1.0 a 107/Z1/2 cm/sec. Over the scale L ^ 108 cm of a granule or a small feature of a sunspot, the merging velocity of two fields is about 103 cm/sec, giving a life L/\vq\ of 105 sec. Over other scales the life varies as Z3/2. It is evident that photospheric fields cannot be annihilated and/or reconnected in less than about 1 day by known mechanisms unless their scale should be considerably less than 103 km. Such hypothetical smaller scale fields are quite unobservable at the present time but would be extremely interesting to explore if it should ever become possible. The main fields of sunspot groups could perhaps be destroyed in periods less than their observed life if oppositely directed fields were pressed together in a suitable way. But there is no observational evidence that this occurs in the photosphere. 2. Chromosphere and corona.—Of great interest in the solar chromosphere is the pos- sibility of annihilating strong magnetic fields so rapidly as to account for the energy re- lease associated with a solar flare. The energy output from a large solar flare seems to be of the order of 1032 ergs, requiring the equivalent of the annihilation of 500 gauss over a cube 2 X 104 km on a side. The really outstanding problem seems to be to understand the mechanism by which a magnetic field might be annihilated and its energy released into the flare phenomenon in the life of 102-103 sec. Consider, then, the optimum circum- stances of two exactly antiparallel magnetic fields pressed firmly together in some region of the solar chromosphere or corona. The magnetic pressure of a 500-gauss field is about 104 dynes/cm2, which is very large compared with the ambient pressure of the chromospheric gas. The gas is strongly com- pressed as it is carried into the transition region. The merging velocity is computed from the value of R given in equation (40). Analysis of flare observations (Jeffries 1957) ; Jeffries et al. 1959; Jeffries and Orrall 1961a, h) suggests that the mean density in the visible flare is perhaps a few times 1011 electrons per cm3, with a temperature somewhere between one and two times 104 ° K.4 Under these conditions the gas, mainly hydrogen, is fully ionized, and ambipolar diffusion is not expected in the region of the visible flare. It then follows from equation (40) that R2 = 3^o/2 and 4 To obtain an upper limit on zj0, put T = 10 ° K. Then the speed of sound a is of the order of 16 km/sec, the density Nm in the transition region between the two 500-gauss fields is 0.7 X 1016/cm3, and er ^ 1013 sec-1. With Ah) = 2 X 10n/cm3, it follows that l/^o = 3.5 X 104. The merging velocity becomes = a 0.6 X 109/T1/2 cm/sec, so that a characteristic scale of Z, = 104 km yields -z^o = 0.2 km/sec, with a = 1. The character- istic life L/dq is 5 X 104 sec, or almost 6 hours, which is much too slow an annihilation to be of much use in producing a flare. The introduction of ambipolar diffusion, which we regard as perhaps dubious in view of the temperatures cited above, adds very little to the merging velocity because of the 4 There are other authors who suggest somewhat higher temperatures (see, for instance, Tandberg- Hanssen and Zirin 1959) which the reader may wish to explore with the formulae given here. © American Astronomical Society • Provided by the NASA Astrophysics Data System SOLAR-FLARE PHENOMENON 205 high value of Nm- Neglecting Joule dissipation and assuming that the fraction of ionized atoms A is uniform across the transition region, put ß = 2 in equation (4). Then £o2 <22 ^irvùMA iWiNn? 2kT vAMA iWiNm and, with Wi = a, a rln(4/iZo)l1/2 = a (56) 31/2L LA^4 íNq J * The temperature must be less than 104 ° K if the gas is to be only partially ionized, so put a = 106 cm/sec. Then A = 10~16 cm2 and A = 10-2 yield î^o = 5 X \.W/L112 cm/sec, which is only seven times larger than for Joule dissipation alone. A scale of L = 104 km yields 1.6 km/sec merging velocity and a characteristic life of 6 X 103 sec, or about 2 hours. This is still too slow to agree with the characteristic flare times of 102-103 sec suggested by observation. It is interesting to note that Gold and Hoyle (1960) in their application of ambipolar diffusion to field annihilation in a flare obtained a characteristic annihilation time of 102 sec. The rapid annihilation which they compute is the result of 12 3 their using a density of 10 neutral atoms per cm for the density Nm in the transition region. This overlooks the requirement that the gas caught between the fields is com- pressed until NkT ~ B2/St, with T < 104 ° K. The ratio of the electron conduction velocity w to the electron thermal velocity wf is readily computed from the order-of-magnitude relation given numerically in equation (50). A temperature of 104 ° K with iVo = 2 X 1011 /cm3 and L = 104 km yields w/w' = 4 X 10-6. Even coronal temperatures, T ^ 106 ° K, and densities No ~ 108/cm3 give w/w' = 2 Y. 10-2. There does not seem to be any possibility here for the runaway elec- trons postulated by Dungey (1961). It is often implied in the literature that the electric field along the length of the transition region leads to an electrical discharge in the vicinity of the neutral line at the center (see, for instance, Sweet 19586; Dungey 1958; Severny 1960). The argu- ment seems to be based on the large total potential difference vqBqL/c that the field represents across the entire width of the region. For instance, a merging velocity of ¿>o = 1 km/sec with a field ¿>o = 5 X 102 gauss means an electric field of 1.6 X 10-3 statvolts/ cm or 0.5 volts/cm. The total potential difference across L = 109 cm is then 5 X 108 volts, which is an imposing number. But it must be remembered that the electric field vqBq/c is just that electric field which is able to produce the electron drift vélocités com- puted in the previous paragraph. And we saw that these velocities are small compared with the electron thermal velocities. Thus there seems to be no indication of anything approaching an electrical discharge, or runaway electrons, or a pinch instability. Finally, note that the merging fields should very soon reach the stationary state treated in the quantitative discussion of Section III because the amount of matter ac- cumulated in the transition region under stationary conditions is only a very small fraction of the total, i.e., lNm<^LNo. The ratio of these two quantities is given by equation (51) for Joule dissipation and is 1.4 X 10-2 for the chromospheric values T = 104°K; iVo = 2 X 10u/cm3; L = 109 cm; and = 5 X 102 gauss. Under coronal conditions of T = 106 ° K and Ao = 108/cm3, the ratio is even smaller, 6 X 10-4. With ambipolar diffusion, equation (53) gives 1 X 10~"2 for 1 per cent ionization, A = 10-2. The length of time required to reach a steady state is, accordingly, not more than about 10~2 Z/z^o, which is so short as to suggest that the merging can never be far from the stationary state during the whole time that the oppositely directed fields are being brought into position for an impending flare. © American Astronomical Society • Provided by the NASA Astrophysics Data System 19 63ApJS. . . .8. .17 7P 4 2 2 32 2 163 43/2 4 2913 2 4 2 25 visible flare.Onthebasisofthisviewitsupposed thattheenergyarisesfromannihila- possibility ofpowerful plasma instabilitiesinthesteepgradientsacross thetransition present timeisthatthisenergyreleasedprincipally inthecentralportionsof remains thepossibilitythat themagneticfieldsatsiteofvisible flare mayconsist region. Eitherofthese might conceivablyenhancethedissipationand annihilationof nomenon, wenotethatthebasicproblemis to constructanenergysourcethatcan enough togivethedesiredfieldannihilation. diffusion ratestotheselarger-scalegradients suggests diffusionrateswhicharelarge from, say,500gausstozero,andtheplasmadensitychangesbyafactorof3X10,from istic scaleofabout5X10cm.Overthismetersthemagneticfieldchanges duced. Itwillbeextremelyinterestingtosee whether theextrapolationoflaboratory not preciselyantiparallel,thenofcoursethese extremegradientsareconsiderablyre- of manyverysmall-scale (10km)fluxtubesofmixedsign,andthere stillremainsthe observation orintheory. Thebestthatcanbesaidforthetheoryis thattherestill tion ofmagneticfields.Weseemtofindvery littlesupportfortheseideaseitherin supply the10ergsthatseemtobeexpendedby alargeflare.Thepopularviewatthe violent small-scalemotionsuchasmightbeassociatedwithanetworkofsmallscale velocity isreducedbyafactoroftheorder10,andcharacteristicreconnection No toN=10/cm,assumingthatthemerging fieldsareantiparallel.Ifthe width ofthetransitionregionisgivenbyequation(44),wherev=â/kire.Witha1, important role.Wearenotinapositiontodecidethisinterestingquestionhere,butwe can computetheconditionsunderwhichsuchinstabilitieswouldhavetooperate.The diffusion. Biermann(1962)hasbeeninterestedinthepossibilitythatinstabilitiesof any meritinthesuggestionatall.Jeffriesetal.(1959)findobservationalevidencefor exchange instabilityacrossthethintransitionregion,ofwidth2/,weretoenhance of manythinropesmagneticfluxoppositesense,thenLmightbeverymuchless flares andactiveregions.If,forinstance,themagneticfieldsinsiteofaflareconsisted for asolarflare.Theknownmechanismsaresufficientlyrapidastobeofinterestinthe type foundinthesteeppressuregradientslaboratoryplasmadevicesmightplayan theoretical investigationwouldberequiredtoconstructsuchamodel,if,infact,thereis than 10km.ThecharacteristicannihilationtimevariesasZ,,sothat,withareduction L couldbeidentifiedwithsomescalesmallerthantheover-all10kmcharacteristicof periods ofperhapsanhourtoadayiftheyarepressedfirmlytogether.Ifthefields annihilation. slow re-formationofsunspotfieldsandquiescentprominences,withobservedlives LV/c, whichis300yearsforL=10cmand Then integration of the equation gives, in the present case, (AS) when Ci is a constant of the integration. Multiplying through by dH/dx and integrating again gives an expression for dF/dx that can be reduced to the quadrature 1 du x (A9) (2^)V4^r0 + where C2 is the second constant of integration. The integral is elliptic and is readily reduced by the substitution 2 2(C2 + C1w-w )V2 to the simple form, ^ ft dj x = 23/4¿1/2 [£(1_ ¿2)]l/2- where £1 = IC-}1'1!(Ci2 + 4C2)l/2. We now let £ = cos2 1/2 2 2 ( C2 + CiF — E ) V4 4> = arccos T (A12) (C^+dC,)1/4 ]• Now suppose that we apply this solution to the asymptotic form of the decay, by ambipolar diffusion, of regions of field of alternate sign. Say that the field vanishes at # = 2nL (n = 0, 1, 2, 3) and is positive in (0, 2Z,), (4L, 6L), etc., and negative in (-2L, 0), (2L, 4L), etc. This is equivalent to the case of oppositely directed fields on each side of æ = 0 confined by im- penetrable boundaries at # = ±L. The boundary conditions are that X(0) = 0 and X'(±L) = 0. In terms of H, this is Hr(Q) = Hn (±L) = 0. Differentiating (A8) with respect to x and re- membering that H was defined so that fí'(O) = 0, it follows that X(0) = 0 requires that = 0. Let BqL§ represent the total flux between rr = 0 and x = L when / = 0. Then it follows that H(L) = and if H"(L) = 0, (A8) requires that Ci = 2Z,<Ï>. It then follows from (All) that 0i = tt/2 and 1^(01, 2~1/2) = K(2l12), £(0i, 2-l/2) = E(2-l/2), in (A10), wherein and E represent the complete elliptic integrals. To obtain an expression for k in terms of L, put x = Lm (A10). Then from (A12) it follows that 0 = 0, and (A10) becomes kL = 21/2<ï>[2E(2-1/2) - K(2~1/2)]2= 1.20$ . Thus, for 0 < £ < L, (A10) becomes 2 2 x= 2£(0, 2-V )-F(0, 2V ) L z£(2~1/2) — K(2~1/2) ‘ © American Astronomical Society • Provided by the NASA Astrophysics Data System 19 63ApJS. . . .8. .17 7P l/3 2 of thexvariation(A15).However,asnotedin thetext,thisveryshortlinearportiondoes c/4:Tcr, wouldhaveintroducedasmalllinearportion inthefieldvariationacrossæ=0,place and The fieldX/&andthefluxH/L$areplottedinFigure8asafunctionofx/L.Toobtainan expression forH(x)inthevicinityofx=0,differentiate(A9),obtaining The expression(A12)for<£mayberewrittenas after takingthe curltoeliminatethegradient terms.Theconstant Xrepresentstheterm netic fieldintherry-plane, thestationaryequationsreduceto not significantlyaffecttheformoffieldelsewhere. Then, ifwe in magneticmodelsofasolarflareoradjacentarms ofthegalaxy. so that decaying byambipolardiffusion.Theexampleillustrates theconfigurationthatmightbefound This, then,istheasymptoticform,plottedinFigure8,ofamagneticfieldalternatingsign 210 sign. l/2 The inclusionofasmallamountresistivity,in the formofdiffusioncoefficientv= Putting v=VXand 5 =VX^zA(47rp)torepresentincompressibleflow andthemag- Fig. 8.—^PlotofthefielddensityX(x)andfluxH(x)acrossstripsmagneticalternating © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem aß Dynamical EquationsforIncompressibleFlow inTwoDimensions expand H/&Lasai(x/L)+ch(x/L).,wereadilyfindthata=§andß 2 d(i>, V$)dU,V,4) d{$,A) d(x, y) d{x, y) d(H_/frL) kLr/BA_/BAAV* = 2V4 d(x/L) $LVL$7VWJ' ^ =arccosj[2(^)-(g)][.(a.4) X(x) ^1.45$ E. N.PARKER APPENDIX II L vV^A =X, (A15) 3> 8 SOLAR-FLARE PHENOMENON 211 To satisfy the first equation, it is sufficient that V2 = /($), V2A = h(A). The second may then be written d(3>, ¿ ) X —vh(A ). d(x, y) This equation requires, in general, that no functional relation exist between and A. The first difficulty encountered in attempting an analytical solution is the problem of determining the functions / and h which correspond to the problem at hand. The problem of incompressible flow in two dimensions is very similar to the problem of in- compressible flow with axial symmetry, discussed at length in Chandrasekhar (1956 and references therein). REFERENCES Athay, R. G., and Moreton, G. E. 1961, Ap. 133, 935. Babcock, H. D. 1959, Ap. 130, 364. Babcock, H. W., and Babcock, H. D. 1955, Ap. 121, 349. Biermann, L. 1962. Private communication. Billings, D. E., and Roberts, W. 0. 1953, Ap. /., 118, 479. Blackwell, D. E., and Ingham, M. F. 1961, M.N., 122, 113. Chandrasekhar, S. 1956, Ap. /., 124, 232. Cowling, T. G. 1953, The Sun, ed. G. P. Kuiper (Chicago: University of Chicago Press). . 1956, M.N., 116, 114. . 1957, Magnetohydrodynamics (New York: Interscience Publishers), pp. 105-12. deFeiter, L. D., and Fokker, A. D. 1961, Bull. Astr. Inst. Netherlands, 15, 319. Dungey, J. W. 1958, Cosmic Electrodynamics (Cambridge: Cambridge University Press), p. 125. . 1961, Kyoto Conf. Cosmic Rays and Earth Storm {IAU), Kyoto, September. Elsässer, W. M. 1954, Phys. Rev., 95, 1. Evans, J. W. 1959, A.J., 64, 330. Fortini, T. 1963, Ap., /., submitted for publication. Gold, T., and Hoyle, F. 1960, M.N., 120, 89. Hale, G. E., Ellerman, F., Nicholson, S. B., and Joy, A. H. 1919, Ap. /., 49, 153. Hanson, R., and Gordon, D. 1960, Pub. A.S.P., 72, 194. Howard, R., and Babcock, H. W. 1960, Ap. J., 132, 218. Hoyle, F., and Wickramasinghe, N. C. 1961, M.N., 123, 51. Jeffries, J. T. 1957, M.N., 117, 493. Jeffries, J. T., and Orrall, F. Q. 1961a, Ap. J., 133, 946. . 19616, ibid., p. 963. Jeffries, J. T., Smith, E. V. P., and Smith, H. J. 1959, Ap. J., 129, 146. Kiepenheuer, K. O. 1953, The Sun, ed. G. P. Kuiper (Chicago: University of Chicago Press). Malitson, H. H., and Webber, W. R. 1962, Solar Proton Manual, ed. F. B. McDonald (Goddard Fields and Particles Preprint Ser., x-611-62-122, Greenbelt, Maryland). Meyer, P., Parker, E. N., and Simpson, J. A. 1956, Phys. Rev., 104, 768. Münch, G. 1953, The Sun, ed. G. P. Kuiper (Chicago: University of Chicago Press). Osterbrock, D. 1961, Ap. J., 134, 347. Parker, E. N. 1957a, Proc. Nat. Acad. Sei., 43, 8. . 19576, J. Geophys. Res., 62, 509. . 1957c, Phys. Rev., 107, 830. . 1961, Ap. J., 133, 1014. . 1962, Space Sei. Rev., 1, 62. Parker, E. N., and Krook, M. 1956, Ap. J., 124, 214. Piddington, J. H. 1954, M.N., 94, 638, 651. Severny, A. B. 1958, Astr. J. SSSR, 35, 335. . 1959, ibid., 36, 972. . 1960, ibid., 37, 609. Spitzer, L. 1956, Physics of Fully Ionized Gases (New York: Interscience Publishers). Sweet, P. A. 1958a, Proceedings of the International Astronomical Union Symposium on Electromagnetic Phenomena in Cosmical Physics, No. 6 (Stockholm, 1956), p. 123. . 19586, Nuovo Cim. Suppl. 8, Ser. X, 188. Tandberg-Hanssen, E., and Zirin, H. 1959, Ap. J., 129, 408. Warwick, J. W. 1955, Ap. J., 121, 376. Weymann, R. 1960, Ap. J., 132, 380. Whitaker, W. A. 1963, Ap. J., in publication. © American Astronomical Society • Provided by the NASA Astrophysics Data System